for all objective functions.
- The normalization is useful for practically all update methods dealing
with constraints (e.g. SQP, MMA). The normalization factor can be either
given explicitly or, if not given, will be the value of the objective
function in the first optimisation cycle.
- The target value is useful when using the objective as a constraint in
constrained optimisation problems (e.g. drag - dragTarget). It should
only be used with update methods that understand the value of the
constraint (e.g. SQP, MMA) but not when the objective in hand is the
only objective of the optimisation problem. In such a case, a squared
objective should be used (e.g. sqr(drag - dragTarget))
- Failed due to double*Matrix<float> multiplication.
Style changes
- use SquareMatrix with Identity on construction
- use Zero in constructors
- remove trailing space and semi-colons
The adjoint library is enhanced with new functionality enabling
automated shape optimisation loops. A parameterisation scheme based on
volumetric B-Splines is introduced, the control points of which act as
the design variables in the optimisation loop [1, 2]. The control
points of the volumetric B-Splines boxes can be defined in either
Cartesian or cylindrical coordinates.
The entire loop (solution of the flow and adjoint equations, computation
of sensitivity derivatives, update of the design variables and mesh) is
run within adjointOptimisationFoam. A number of methods to update the
design variables are implemented, including popular Quasi-Newton methods
like BFGS and methods capable of handling constraints like loop using
the SQP or constraint projection.
The software was developed by PCOpt/NTUA and FOSS GP, with contributions from
Dr. Evangelos Papoutsis-Kiachagias,
Konstantinos Gkaragounis,
Professor Kyriakos Giannakoglou,
Andy Heather
[1] E.M. Papoutsis-Kiachagias, N. Magoulas, J. Mueller, C. Othmer,
K.C. Giannakoglou: 'Noise Reduction in Car Aerodynamics using a
Surrogate Objective Function and the Continuous Adjoint Method with
Wall Functions', Computers & Fluids, 122:223-232, 2015
[2] E. M. Papoutsis-Kiachagias, V. G. Asouti, K. C. Giannakoglou,
K. Gkagkas, S. Shimokawa, E. Itakura: ‘Multi-point aerodynamic shape
optimization of cars based on continuous adjoint’, Structural and
Multidisciplinary Optimization, 59(2):675–694, 2019
A set of libraries and executables creating a workflow for performing
gradient-based optimisation loops. The main executable (adjointOptimisationFoam)
solves the flow (primal) equations, followed by the adjoint equations and,
eventually, the computation of sensitivity derivatives.
Current functionality supports the solution of the adjoint equations for
incompressible turbulent flows, including the adjoint to the Spalart-Allmaras
turbulence model and the adjoint to the nutUSpaldingWallFunction, [1], [2].
Sensitivity derivatives are computed with respect to the normal displacement of
boundary wall nodes/faces (the so-called sensitivity maps) following the
Enhanced Surface Integrals (E-SI) formulation, [3].
The software was developed by PCOpt/NTUA and FOSS GP, with contributions from
Dr. Evangelos Papoutsis-Kiachagias,
Konstantinos Gkaragounis,
Professor Kyriakos Giannakoglou,
Andy Heather
and contributions in earlier version from
Dr. Ioannis Kavvadias,
Dr. Alexandros Zymaris,
Dr. Dimitrios Papadimitriou
[1] A.S. Zymaris, D.I. Papadimitriou, K.C. Giannakoglou, and C. Othmer.
Continuous adjoint approach to the Spalart-Allmaras turbulence model for
incompressible flows. Computers & Fluids, 38(8):1528–1538, 2009.
[2] E.M. Papoutsis-Kiachagias and K.C. Giannakoglou. Continuous adjoint methods
for turbulent flows, applied to shape and topology optimization: Industrial
applications. 23(2):255–299, 2016.
[3] I.S. Kavvadias, E.M. Papoutsis-Kiachagias, and K.C. Giannakoglou. On the
proper treatment of grid sensitivities in continuous adjoint methods for shape
optimization. Journal of Computational Physics, 301:1–18, 2015.
Integration into the official OpenFOAM release by OpenCFD
